WASHINGTON — The two most influential social liberals in President Trump’s inner circle — daughter Ivanka and son-in-law Jared Kushner — helped kill a proposed executive order that would have scrapped Obama-era L.G.B.T. protections, according to people familiar with the issue.

A third, Gary D. Cohn, the chairman of the president’s National Economic Council, a Democrat who was brought to the West Wing by Mr. Kushner and reflects the socially liberal and economically conservative views of many Wall Street power brokers, privately told aides to the president that he was disturbed it was even being considered.

The executive order has exposed what is likely to be a persistent schism in Mr. Trump’s paradoxical presidency: He is a cosmopolitan New Yorker who has long operated in an environment where sexual orientation is often an afterthought, but is nonetheless beholden to the social conservatives who backed him overwhelmingly in 2016, despite reports of his crudeness and sexual misdeeds.

Mr. Kushner, a lifelong Democrat, and Ms. Trump, an independent, travel in liberal social circles and have long supported L.G.B.T. rights. Neither had seen the order before details were leaked. They expressed their dissatisfaction to Mr. Trump’s other advisers, and then weighed in directly with the president, who opposes same-sex marriage but has spoken out against discrimination.

On Monday night, reports had swirled that Mr. Trump would sign some version of the rollback as a concession to social conservatives ahead of the president’s announcement of a United States Supreme Court nominee. As a result, White House officials pushed out a statement asserting that Mr. Trump “is determined to protect the rights of all Americans, including the L.G.B.T.Q. community,” adding that the president “continues to be respectful and supportive of L.G.B.T.Q. rights, just as he was throughout the election.”

The draft order, circulated by religious conservatives allied with Mr. Trump and Vice President Mike Pence, was one of about 250 edicts that have been sent to federal agencies for vetting.

Mr. Trump never seriously considered signing the order, and did not need much convincing, people close to him said.

Still, conservatives inside the Trump camp pressured the president to consider a version of a “religious freedom” measure, similar to one supported by Mr. Pence in 2015 while he was the governor of Indiana, according to two senior administration officials.

Mr. Pence, however, did not personally push for the White House order, according to one of his allies.

Mr. Kushner and Ms. Trump’s opposition to the draft was first reported by Politico. It came on the heels of an announcement by the Nordstrom department store chain that it will scale back on featuring Ms. Trump’s clothing line from its stores, a public blow to a brand she has spent years cultivating.

A day after the White House quashed the religious freedom order, at the National Prayer Breakfast in Washington, Mr. Trump offered religious conservatives an olive branch by proposing to eliminate a law that bars churches with Internal Revenue Service charity designations from making political endorsements.

Some conservative leaders warned Mr. Trump that his decision to retain former President Barack Obama’s order on L.G.B.T. rights could have far-reaching political implications. “Our base would want to know who is responsible for what we believe is an issue of religious liberty — that would be of concern to us,” said Bob Vander Plaats, the chief executive of The Family Leader, a socially conservative organization.

“We have been consistent,” Mr. Vander Plaats added. “We’ve cheered President Trump a lot. But on this one, our base is wondering why Obama’s executive order would be allowed to stand?”

Tony Perkins, the president of the conservative Family Research Council, backed the draft order and said he believed Mr. Trump’s opposition was only temporary. He pointed out that evangelicals were supportive of Mr. Trump during the campaign, and that there would need to be reconciliation between his support for religious liberty and his decision to uphold the L.G.B.T. order.

“He gets it,” Mr. Perkins said of the president. “They will have to fix it and they will. I’m confident they will. Am I concerned? No. Not at this point.”

The topic of the order was a sensitive one in a West Wing that prides itself on decisiveness and bombast.

“There are a lot of ideas that are being floated out,” Sean Spicer, the White House press secretary, told reporters on Thursday. “Part of it is, the president does all the time, he asks for input, he asks for ideas. And on a variety of subjects there are staffing procedures that go on where people have a thought or an idea and it goes through the process.”

A version of this article appears in print on , on Page A10 of the New York edition with the headline: Ivanka Trump and Her Husband Help to Thwart Rollback of Gay Rights. Order Reprints | Today’s Paper | Subscribe